Robust variance estimators for generalized regression estimators in cluster samples

Standard linearization estimators of the variance of the general regression estimator are often too small, leading to confidence intervals that do not cover at the desired rate. Hat matrix adjustments can be used in two-stage sampling that help remedy this problem. We present theory for several new variance estimators and compare them to standard estimators in a series of simulations. The proposed estimators correct negative biases and improve confidence interval coverage rates in a variety of situations that mirror ones that are met in practice.